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The principal block of a ${\mathbb Z}_{\ell}$-spets and Yokonuma type algebras

Radha Kessar, Gunter Malle and Jason Semeraro

Vol. 17 (2023), No. 2, 397–433
Abstract

We formulate conjectures concerning the dimension of the principal block of a -spets (as defined in our earlier paper), motivated by analogous statements for finite groups. We show that these conjectures hold in certain situations. For this we introduce and study a Yokonuma type algebra for torus normalisers in -compact groups which may be of independent interest.

Keywords
$\ell$-adic reflection groups, Yokonuma type algebra, principal block, spetses
Mathematical Subject Classification
Primary: 16G30, 20C08, 20C20, 20F55, 20G40
Secondary: 20D20, 55R35
Milestones
Received: 30 June 2021
Revised: 9 March 2022
Accepted: 11 April 2022
Published: 24 March 2023
Authors
Radha Kessar
Department of Mathematics
City, University of London
London
United Kingdom
Gunter Malle
Fachbereich Mathematik
TU Kaiserslautern
Kaiserslautern
Germany
Jason Semeraro
Heilbronn Institute for Mathematical Research, Department of Mathematics
University of Leicester
Leicester
United Kingdom

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